President Carter reclaimed the Democratic nomination tonight and, reaching out to his defeated party rival, appealed to Sen. Edward M. Kennedy to help him turn back the "alarming, even perilous" prospect of a Ronald Reagan Republican presidency.

In an acceptance speech he will use in his campaign against his GOP opponent, Carter told the Democratic National Convention and a national television audience that in November Americans will make a fundamental choice between "two futures," one based on reality and the other made up of "a world of fantasy."

The carefully orchestrated climax of the convention -- where the president controlled the delegates' votes but onlyKennedy captured their emotions -- came as the Massachusetts senator joined Carter at the podium for the long-awaited public display of reconciliation.

The moment had little of the emotion generated by Kennedy in his speech here Tuesday night. But it provided a brief lift to a demonstration for Carter that fell flat shortly after it began.

Kennedy did his duty by appearing on the podium, but he seemed wooden and kept his distance from Carter.

A few minutes earlier, in a speech that did not match Kennedy's performance two nights ago and that never seemed to arouse the crowd in Madison Square Garden, the president told the convention and the nation that the country is at a time that "can transform both our personal lives and the life of our country."

"The choice -- the choice between the two paths to the future -- could not be more clear," he said. "If we succumb to a world of fantasy, we will wake up to a nightmare.But if we start with reality and fight to make our dreams a reality, all Americans will have a good life, a life of meaning and purpose in a nation strong and secure."

Carter's acceptance speech, the start of the president's uphill battle against his Republican rival, was an attempt to put the bitter primary contest with Kennedy behind the Democratic Party and make Reagan the issue in the fall campaign.

Just before Carter began speaking, William Winpisinger, president of the International Association of Machinists, led a walkout of more than 100 delegates protesting the president's failure to offer stronger support for some of the economic planks in the platform. A number of other delegates walked out during the speech.

There was another display of anger about Carter policies when some delegates booed the president's mention of his call for draft registration in response to the Soviet invasion of Afthanistan. But the overwhelmingly pro-Carter crowd quickly drowned out the boos with cheering and a chant of "We want Jimmy."

The president did not mention Reagan by name. But in extraordinary tribute to the special place Kennedy holds in the liberal wing of the party, Carter made a personal appeal to the Massachusetts senator to join him in the battle against the GOP nominee.

Declaring that Kennedy's speech to the convention Tuesday night "was a magnificent statement of what the Democratic Party has meant to the people of our country and why a Democratic victory is so important this year," Carter said:

"I reach out to you tonight and to those who supported you in your valiant and passionate campaign. Ted, your party needs -- and I need -- your idealism and dedication working for us. There is no doubt that even greater service lies ahead of you, and we are grateful to have your strong partnership now in the larger cause to which your own life has been dedicated."

White House officials said Carter's address deliberately was not "a stump speech" aimed at the delegates in the hall, but an effort to focus the voting public on the fundamental issues in the campaign as he sees them.

Mondale's acceptance speech was couched in rally language and was designed for the partisan crowd.

The two speeches was drafted in tandem.

The purpose of the Carter speech, these officials said, was to contrast the future of the country under Carter's and Reagan's leadership.

By a design, independent candidate John B. Anderson, whose campaign is regarded as a threat to draw off votes from Carter, was not mentioned -- or even indirectly acknowledged.

Officials said the speech had gone through six drafts, with chief speech-writer Hendrik Hertzberg shuttling between New York and Camp David, Md., early this week to work out the final adjustments between Carter and his advisers.

They said the president has spent as much time on this speech as any of his career. After working over it most of the weekend and the early part of the week at Camp David, Carter gave it his final approval at 4:30 p.m. today, then took a nap.

At the convention's close, delegates spoke favorably about Carter's acceptance speech, but their enthusiasm was notably restrained. Carter delegates said it was good because it was truthful and straightforward; Kennedy delegates said it was good, but it wasn't Kennedy.

"I thought it was great because it was realistic," said Ann J. Land, a Carter delegates from Philadelphia. "It gave us hope for progress for the future." Nearby, Kennedy delegate Boyd McGranaghan of Dary Township, Pa., offered moderate praise for the speech.

"Well Carter's speech was better than Jerry Brown's but not as good as Hugh Carey's," he said. "And it did come close to Ted Kennedy's. But ther president spoke well for healing the party -- and he spoke well for Ted -- and that's important."

In the Minnesota delegation, Carter's state chairman, Attorney General Warren Spannus, said: "It was a terrific speech. He told us what the problems were. He didn't try to fool anyone out here. And That's one thing the American people appreciate."

Behind him, Peter McLaughlin, a Kennedy delegate from Minneapolis, said, "It's tough for anyone to follow a Ted Kennedy speech. But the president did well. He talked about the future and he attacked Ronald Reagan. And that's what we need to do."

Carter delegate John Kerr of Pennsylvania said, "I thought it was a great speech . . . Well, not as inspiring as Ted's, but it did a good job of setting out the agenda for the campaign."

Paul DeGrandis of Cleveland, Ohio, said of the speech: "I think it was very good in terms of party until. It was definitely not his best speech."

"It was good enough," said Carter partisan George Hunter of the Minnesota delegation. "It could have been a little more hellfire and brimstone [against the Republicans] . . . We're united now."

Written off by many in his own party as a sure loser 10 months ago, Carter strode to the podium in Madison Square Garden at 10:20 tonight to claim the nomination he first accepted in the same place four years ago. For a moment he simply stood looking out, drinking in the scene before him, a sea of chanting Democrats waving Carter signs. It was a scene many of his strongest supporters thought he would never see in 1980.

Just as the president was beginning his speech, there was a disturbancce on the convention floor when a string of firecrackers began exploding. The incident may have rattled Carter, who was paying tribute to the late Senator Hubert Humphrey of Minnesota, whom he referred to as "Hubert Horatio Hornblower." The firecrackers apparently were set off by a woman who shouted that she was a member of the Communist Workers Party.

Carter clearly hopes to turn his theme of "the two futures" into the central campaign issue of the fall in which he represents a future of "economic security . . . peace . . . and justice" and Reagan offers a far darker prospect.

"In that other future," the president said, "I see despair -- the despair of millions who would have to struggle for equal opportunity and a better life. o

"I see surrender -- the surrender of our energy future to the merchants of oil.

"I see risk -- the risk of international confrontation, the risk of an uncontrollable, unaffordable and unwinable nuclear arms race."

He did not believe, the president said, that Reagan seeks such a future for the country.

"But I do question the disturbing commitments and policies already made by him and by those with him who have now captured control of the Republican Party," he said. "The consequences of those commitments and policies would drive us down the wrong road. It is up to all of us to make sure America rejects this alarming, even perilous destiny."

The future that Reagan and the Republicans offer is dangerous, Carter said, because their vision is grounded in "a world of tinsel and make-believe . . . a fantasy world."

The president defended his record and on every issue he mentioned contrasted that with what he said Reagan proposes.

While the administration is rebuilding the military and remains commited to nuclear arms control, "the new leaders of the Republican Party, in order to close the gap between their rhetoric and their record, have now promised to launch an all-out nuclear arms race," he said.

When the administration moved to counter the Soviet invasion of Afghanistan, Reagan opposed the U.S. grain embargo and the Olympic boycott, the president noted.

Reagan "does not seem to know what to do with the Russians,' Carter said. "He is not sure if he wants to feed them, play with them or fight with them."

While the administration is moving "to secure America's energy future," Reagan proposes only to "unleash the oil companies and let them solve the energy problem for us."

On what is likely to be the most critical issue of the fall campaign -- the economy -- the president acknowledged that "the road has been bumpy" in seeking to control inflation and stimulate the economy. But Reagan's only solution, he said, is to propose a 30 percent tax cut over three years, "the biggest tax giveaway in American history."

Carter was preceded to the podium by Mondale, who delivered a slashing attack on Reagan, and the delegates joined in chanting his lines of denunciation.

Reciting a litany of what "most Americans believe . . . but not Ronald Reagan," Mondale said "the Republican nominee wants us to forget all he stands for -- 40 years of extreme positions."

Reagan's beliefs, the vice president said, "are alien to everything I know about America. That negative thinking was not part of the small towns of rural Minnesota where I grew up . . . That tone of resentment was never heard in my father 's church. That cynicism was not what I felt in the high schools, the farms, the factories and the homes that I've visited all over the nation in the last 3 1/2 years."

Soon after Mondale finished speaking, Madison Square Garden was sealed off by police in riot gear. Hundreds of delegates, many of them bewildered or angry, were refused admission to the convention center by police who bluntly told them to clear the sidewalk.

Police concern appeared to have been sparked by a demonstration of the Communist Workers Party that was stopped, with some violence, two blocks from the Garden.

The Associated Press reported that 22 of the demonstrators were arrested and 19 police officers were hurt.

As the final session got under way, Mondale was renominated for vice president by United Auto Workers President Douglas A. Fraser, a leading Kennedy backer, who hailed the Minnesotan as a "progressive voice" needed in the Carter administration.

"Ted Kennedy and Walter Mondale are the same kind of Democrat," said Fraser, who is expected to help lead reconciliation efforts between the Carter and Kennedy camps. "Ted Kennedys voting record in the U.S. Senate and that of Fritz Bondale were virtually identical."

Speaking from the liberal wing of the Democratic Party, Fraser said the party faces an "uphill battle" against Reagan but can win if it remains "the party of compassion . . . the party of equality . . . the party of economic and social justice."

But he also stressed party reconciliation, noting that Republicans have found unity, and adding, "If the right wing has enough sense to unify, so should we."

Delegates milled about the floor of the convention hall during the ritualistic roll call verifying Mondale's renomination. A scattering of votes was thrown to other political figures who had not been nominated. One mischievous Kennedy delegate, undoubtedly looking ahead and hoping the senator will try again for the nomination, cast his vote for George Orwell, author of the novel "1984."

Otherwise, the early part of the evening went according to the script as the convention renominated the ice president by acclamation and the band struck up "The Minnesota Rouser."

Convention officials filled the hours leading up to the prime-time television appearances by Mondale and Carter with a tribute to dead Democrats and speeches by Arkansas Gov. Bill Clinton, House Majority Leader Jim Wright (D-Tex.), Senate Majority Leader Robert C. Byrd (D-W.Va.) and others.

At a convention curiously dominated by the comings, goings and intentions of the loser, Kennedy, this finally was Carter's day.

He left his Manhattan hotel headquarters at 6 a.m. for a two-mile jog in Central Park and later excorted his wife to the Stage Delicatessen for a breakfast of Swiss cheese omelette and bagels with cream cheese.

According to Carter, all was well between him and Kennedy at the end of their long and sometimes bitter contest for the nomination.

"I've several telephone calls to and from Sen. Ted Kennedy [and] we've kept a close, amicable, constructive relationship," the president told reporters.

At midday Carter spoke to Democratic politicians and their prosperous supporters at a $500-a-plate "Victory Lunch" in the Plaza hotel.

He told them there had never been a president -- including Franklin D. Roosevelt and Lyndon B. Johnson-- "who has had a better record of support from the Congress than Jimmy Carter." The news media do not understand this record of accomplishment, Carter said, so "the people who look at and listen to the news media" do not understand it either. He promised to deliver the message during the fall campaign.

Carter said his first term had laid the basis for a new, golden age of American prosperity. "The prospect of that . . . can transform the American electorate," he said.

He repeatedly assured his audience that he would win in November.

A Democratic victory, Carter told the luncheon, "will be one of the greatest accomplishments of all time."

He acknowledged that his administration had faced difficulties, but said it was operating in "the most complicated, complex, rapidly changing world that human beings have even seen."

The tableau of political unity that unfolded on the podium of Madison Square Garden tonight climaxed four days of convention acivity that were probably as good as the beleaguered president could expect.

When the convention opened Monday, Carter was assured the nomination but little else. He was the clear winner over Kennedy, but his party was divided and the dissatisfaction with his candidacy was best summed up by the last-minute demands for an "open" convention, another way of saying "dump Carter."

The president left Madison Square Garden tonight by no means asssured of the backing of a truly unified party and far from a beloved figure among his fellow Democrats. But the Democrats seemed at least to have met keynote speaker Morris K. Udall's call for a brief coming together of the waring factions to preserve their "fighting chance" against Reagan in November.

Kennedy played a critical role in achieving this. His abrupt withdrawal from the race Monday night after he lost the key open convention rules fight left his supporters dispirited, infecting the gathering with a sense of gloom.

What Kennedy did here -- playing the role of loser on the national stage of a political convention -- was critical to the underdog president's "fighting chance." The political pros around Carter bet from the beginning that Kennedy would be there when they needed him, and they were not disappointed.

The Massachusetts senator's speech Tuesday night transformed the atmosphere of the convention, for while he made clear his differences with Carter over the economy, he had far harsher things to say about Reagan. His endorsement of the president and pledge to work for the ticket in the fall, read to the convention by his ally from Massachusetts, House Speaker Thomas P. (Tip) O'Neill Jr., was the ideal capstone for Carter's triumph after the convention roll call Wednesday night.

Kennedy played his role in the high political drama to the hilt, providing an element of suspense and theater to an event with an ordained outcome. Whatever his motives -- he did nothing to discourage speculation that he will make another run for the nomination in 1984 -- he gave Carter what he needed.

And the Carter forces here demonstrated again that they are, above all things, pragmatists in the art of politics. Their sudden capitulation to most of Kennedy's demands on the economy planks in the platform was a recognition of political reality and the importance of Kennedy and his supporters not just in holding the convention together but in winning the fall election.

Still, amid all the cheering that rang down the curtain on the 1980 convention, there was no concealing the difficult task facing the president. California Gov. Edmund G. (Jerry) Brown Jr., an early victim of Carter's primary victories, pledged his support and said of Carter, "His fight is our fight."

But, Brown added, "It's not going to be easy. He needs to project an aura of competence, and he needs some luck."